It is a cultural thing that is probably left over from the colonization era. Things will change but it takes time.
He being an American of generally liberal persuasion tried, as your family did, to treat the cook and gardener as 'equals'.
Over time that changed though. One day the maid sat him down and politely explained that it was sort of insulting to be treated too familiar in this context. She was speaking of the gardener and said, "What you are doing makes him feel very uncomfortable". She explained, "the old man there is kneeling in your garden pulling weeds 8 hours a day, and you come home...breeze in in your 50K auto and ask him if he wants to share a beer with you..."
He realized she was right. These people were not "passionate about their career", in fact there was no career, nor even the semblance of it. They were just doing whatever possible work they could do to earn enough money to keep food on their families table. Treating them too familiar, or even implying they shared lots of things in common, was sort of demeaning.
In the end, he wound up treating them very formally. "Sr Veracruz" "Sra Sanchez" etc...always keeping a sort of respectful distance between them. Posting work schedules, etc and generally treating them like employees.
I'm not at all against what you said, nor implying you guys didn't do what was right, simply showing there are more than one interpretation of such situations.
in china, nanny's are generally relatives. the grandparents, an aunt or a cousin. so they are part of the family. they are there because they are genuinely needed to share the work, there is no class difference. only when relatives are not available, someone else is hired, but their status is not much different.
Assuming you are paying a fair salary, other cultures/countries don't have a housekeeper (even as a part-time work) because they cannot afford one not because it is an ethical or moral thing. In general, families with children need a lot of extra help when parents work.
I used to have a maid come in for about 4 hours once a week. She'd do all of our laundry, clean the house, wash whatever dishes were dirty, etc. She had a number of customers like us, plus one that'd pay her a set amount per month to come every day for a couple hours a day and clean/cook dinner. She was making about R$2,000 a month plus her retirement. It was a pretty decent amount, when a good salary for people my age was around R$3,000.